-
Notifications
You must be signed in to change notification settings - Fork 761
/
mixture_gaussian_mh.py
85 lines (69 loc) · 2.62 KB
/
mixture_gaussian_mh.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
#!/usr/bin/env python
"""Mixture of Gaussians.
Perform inference with Metropolis-Hastings. It utterly fails. This is
because we are proposing a sample in a high-dimensional space. The
acceptance ratio is so small that it is unlikely we'll ever accept a
proposed sample. A Gibbs-like extension ("MH within Gibbs"), which
does a separate MH in each dimension, may succeed.
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import edward as ed
import numpy as np
import six
import tensorflow as tf
from edward.models import \
Categorical, Dirichlet, Empirical, InverseGamma, Normal
from scipy.stats import norm
def build_toy_dataset(N):
pi = np.array([0.4, 0.6])
mus = [[1, 1], [-1, -1]]
stds = [[0.1, 0.1], [0.1, 0.1]]
x = np.zeros((N, 2), dtype=np.float32)
for n in range(N):
k = np.argmax(np.random.multinomial(1, pi))
x[n, :] = np.random.multivariate_normal(mus[k], np.diag(stds[k]))
return x
N = 500 # number of data points
K = 2 # number of components
D = 2 # dimensionality of data
ed.set_seed(42)
# DATA
x_data = build_toy_dataset(N)
# MODEL
pi = Dirichlet(alpha=tf.constant([1.0] * K))
mu = Normal(mu=tf.zeros([K, D]), sigma=tf.ones([K, D]))
sigma = InverseGamma(alpha=tf.ones([K, D]), beta=tf.ones([K, D]))
c = Categorical(logits=tf.tile(tf.reshape(ed.logit(pi), [1, K]), [N, 1]))
x = Normal(mu=mu[c], sigma=sigma[c])
# INFERENCE
T = 5000
qpi = Empirical(params=tf.Variable(tf.ones([T, K]) / K))
qmu = Empirical(params=tf.Variable(tf.zeros([T, K, D])))
qsigma = Empirical(params=tf.Variable(tf.ones([T, K, D])))
qc = Empirical(params=tf.Variable(tf.zeros([T, N], dtype=tf.int32)))
gpi = Dirichlet(alpha=tf.constant([1.4, 1.6]))
gmu = Normal(mu=tf.constant([[1.0, 1.0], [-1.0, -1.0]]),
sigma=tf.constant([[0.5, 0.5], [0.5, 0.5]]))
gsigma = InverseGamma(alpha=tf.constant([[1.1, 1.1], [1.1, 1.1]]),
beta=tf.constant([[1.0, 1.0], [1.0, 1.0]]))
gc = Categorical(logits=tf.zeros([N, K]))
inference = ed.MetropolisHastings(
latent_vars={pi: qpi, mu: qmu, sigma: qsigma, c: qc},
proposal_vars={pi: gpi, mu: gmu, sigma: gsigma, c: gc},
data={x: x_data})
inference.initialize()
sess = ed.get_session()
init = tf.global_variables_initializer()
init.run()
for _ in range(T):
info_dict = inference.update()
t = info_dict['t']
if t == 1 or t % inference.n_print == 0:
accept_rate = info_dict['accept_rate']
print("iter {:d} accept rate {:.2f}".format(t, accept_rate))
print("Inferred membership probabilities:")
print(sess.run(qpi.mean()))
print("Inferred cluster means:")
print(sess.run(qmu.mean()))